The present invention relates to a method and apparatus for compensation of charging current in electrochemical cells, and, more particularly, to real-time double layer current correction using a differential sample/hold technique.
FIG. 1 shows an equivalent circuit of a typical electrochemical cell. The three electrode cell arrangement is now routinely used. Current is furnished to the cell through a counter electrode, and the potential difference between the reference and working electrode is monitored.
There are two types of current in electrochemical cells: 1) faradaic current, and, 2) double layer charging (capacitive) current. Electrochemists are mainly concerned with measuring faradaic current, i.sub.f, unless a study of the double-layer capacitance is being done. Faradaic current, i.sub.f, is current which passes through the faradaic impedance, Z.sub.f, and is due to movement of electrons across the electrode/solution interface. Faradaic currents arising because of redox processes do not affect the analysis.
There is also double layer charging current, i.sub.c, in electrochemical cells. At an ideally polarized electrode, the potential across the electrode/solution interface changes and charge flows in an amount required by changes in solute populations adjacent to the electrode solution interface. Charge is accumulated at the electrode/solution interface as the applied potential is varied due to the accumulation or deficiency of electrons at the electrode/solution interface required by changes in the solution ion and dipole populations adjacent to the electrode/solution interface. The separation of charge normal to the electrode/solution interface gives the interface the property of an electrical double-layer and is represented as a double-layer capacitance, C.sub.dl, in FIG. 1. The accumulation of charge at the electrode solution interface creates charging current in electrochemical cells.
Charge flow is described by Equation 1 as follows: EQU dq.sub.e =A{C.sub.dl (E)}dE (Eq. 1)
where
dq.sub.e is the differential charge flow across the electrode solution interface, accompanying a differential change in potential, PA1 A is the electrode area, PA1 dE is the differential potential difference across the electrode/solution interface, and, PA1 C.sub.dl is the differential double-layer capacitance.
The double-layer capacitance is shown as a function of E because the relationship between charge and potential for the electrochemical capacitor is not generally linear.
Current measuring devices measure the sum of faradaic plus charging current. When the charging current becomes a limiting factor in obtaining analytical information, it becomes necessary to compensate or correct for charging current. The problem is to somehow measure and then filter out or isolate the charging current component of the working electrode current to enable an accurate and precise measurement of the faradaic current component.
Many approaches for correcting or compensating for charging current are known in the art. Mathematical methods of charging current correction do not attempt real-time correction for charging current. Mathematical calculations are made after the experiment is performed to remove the unwanted effect of charging current. Known mathematical techniques include curve-fitting methods, Kalman filter, and Cottrell filtration. A disadvantage of curve-fitting techniques is that they usually require a complex, mathematical model for every system studied, and the system must be thoroughly understood. The Cottrell filtration is assumed to contain only charging current as extraneous current; in fact, extraneous currents due to noise, non-linear diffusion and sphericity contributions to the measured current are also present.
Another mathematical method is the derivative method, which plots the derivative of the current with respect to time versus the applied potential. Assuming the differential double-layer capacity is independent of potential, the first derivative of the charging current with respect to time is equal to zero. Hence, there is no contribution of charging current under linear scan voltammetric LSV conditions. The disadvantage of this method is that it is dependent upon the differential double-layer capacitance being constant over the applied potential range. Unfortunately, the double-layer capacitance does change with applied potential.
Other techniques for correcting for charging current are based on response differences between faradaic current and charging current. These techniques do not eliminate charging current, but take into account the presence of charging current and appropriately alter experimentation to yield results which are relatively free from the effects of charging current. These techniques include AC voltammetry and potential step techniques.
Yet another method is the background subtraction method of charging current correction, which subtracts the residual current from the total current. This method subtracts charging current, current caused by impurities in solution, and current due to oxidation or reduction of the electrolyte from the total measured current. A disadvantage of this method is that it usually requires two separate and duplicate experiments, and assumes the charging current in the first experiment is equal to that in the second.
Thus, a need has existed for a real-time instrument correction or compensation of charging current while the experiment is taking place. A need has also existed for a real-time technique which accounts for the charging double-layer capacitance as a function of potential.